Question

select the expression that is equivalent to \\((x + 4)^2\\).

\\(\bigcirc\\) a. \\(2x + 8x + 16\\)

\\(\bigcirc\\) b. \\(x^2 + 8x^2 + 16\\)

\\(\bigcirc\\) c. \\(x^2 + 4x + 16\\)

\\(\bigcirc\\) d. \\(x^2 + 8x + 16\\)

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = x\) and \(b = 4\).

Step2: Apply the formula

Substitute \(a = x\) and \(b = 4\) into the formula:

• \(a^2 = x^2\)
• \(2ab = 2\times x\times4 = 8x\)
• \(b^2 = 4^2 = 16\)

So, \((x + 4)^2 = x^2 + 8x + 16\).

Answer:

D. \(x^2 + 8x + 16\)